R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
ICML '06 Proceedings of the 23rd international conference on Machine learning
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
A Unified View of Matrix Factorization Models
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on gait analysis
Large margin classifiers based on affine hulls
Neurocomputing
Distance metric learning by minimal distance maximization
Pattern Recognition
Robust principal component analysis?
Journal of the ACM (JACM)
Subspace embeddings for the L1-norm with applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Improve robustness of sparse PCA by L1-norm maximization
Pattern Recognition
Emerging topic detection using dictionary learning
Proceedings of the 20th ACM international conference on Information and knowledge management
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Block principal component analysis with L1-norm for image analysis
Pattern Recognition Letters
Robust principal component analysis with non-greedy l1-norm maximization
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Towards a robust framework of network coordinate systems
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part I
Low-rank matrix decomposition in L1-norm by dynamic systems
Image and Vision Computing
A probabilistic approach to robust matrix factorization
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
General and nested wiberg minimization: L2 and maximum likelihood
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Hyperdisk based large margin classifier
Pattern Recognition
Euler Principal Component Analysis
International Journal of Computer Vision
Generalization of linear discriminant analysis using Lp-norm
Pattern Recognition Letters
Feature extraction based on Lp-norm generalized principal component analysis
Pattern Recognition Letters
Face hallucination based on sparse local-pixel structure
Pattern Recognition
DMFSGD: a decentralized matrix factorization algorithm for network distance prediction
IEEE/ACM Transactions on Networking (TON)
A robust elastic net approach for feature learning
Journal of Visual Communication and Image Representation
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Matrix factorization has many applications in computer vision. Singular Value Decomposition (SVD) is the standard algorithm for factorization. When there are outliers and missing data, which often happen in real measurements, SVD is no longer applicable. For robustness Iteratively Re-weighted Least Squares (IRLS) is often used for factorization by assigning a weight to each element in the measurements. Because it uses L驴 norm, good initialization in IRLS is critical for success, but is non-trivial. In this paper, we formulate matrix factorization as a L驴 norm minimization problem that is solved efficiently by alternative convex programming. Our formulation 1) is robust without requiring initial weighting, 2) handles missing data straightforwardly, and 3) provides a framework in which constraints and prior knowledge (if available) can be conveniently incorporated. In the experiments we apply our approach to factorization-based structure from motion. It is shown that our approach achieves better results than other approaches (including IRLS) on both synthetic and real data.